Intuitive understanding of extinction of small particles in absorbing and active host media within the MLWA

In an absorbing or an active host medium characterized by a complex refractive index $n_2=n_2^{\mathrm{\prime }}+\mathrm{i}{n}_2^{\mathrm{\prime }\mathrm{\prime }}$, our previously developed modified dipole long-wave approximation (MLWA) is shown to essentially overly with the exact Mie theory results for spherical nanoparticle with radius $a\lesssim 25$ nm ($a\lesssim 20$ nm) in the case of Ag and Au (Al and Mg) nanoparticles. The agreement for Au and Ag (Al and Mg) nanoparticles, slightly better in the case of Au than Ag, continues to be acceptable up to $a\sim 50$ nm ($a\sim 40$ nm), and can be used, at least qualitatively, up to $a\sim 70$~nm ($a\sim 50$ nm) correspondingly. A first order analytic perturbation theory (PT) in a normalized extinction coefficient, $\bar{\kappa }=n_2^{\mathrm{\prime }\mathrm{\prime }}\mathrm{/}{n}_2^{\mathrm{\prime }}$, around a nonabsorbing host is developed within the dipole MLWA and its properties are investigated. It is shown that, in a suitable parameter range, the PT can reliably capture the effect of host absorption or gain on the extinction efficiency of various plasmonic nanoparticles.